import enum from tqdm_loggable.auto import tqdm import jax import jax.numpy as jnp from jax import jit from jax.flatten_util import ravel_pytree from varipeps import varipeps_config from varipeps.config import Line_Search_Methods, Wavevector_Type from varipeps.ctmrg import CTMRGNotConvergedError, CTMRGGradientNotConvergedError from varipeps.peps import PEPS_Unit_Cell from varipeps.expectation import Expectation_Model from varipeps.mapping import Map_To_PEPS_Model from varipeps.utils.debug_print import debug_print from .inner_function import ( calc_ctmrg_expectation, calc_preconverged_ctmrg_value_and_grad, calc_ctmrg_expectation_custom_value_and_grad, ) from typing import Sequence, Tuple, List, Union, Optional, Dict @jit def _scalar_descent_grad(descent_dir, gradient): descent_dir_real, _ = ravel_pytree(descent_dir) gradient_real, _ = ravel_pytree(gradient) if jnp.iscomplexobj(descent_dir_real): descent_dir_real = jnp.concatenate( (jnp.real(descent_dir_real), jnp.imag(descent_dir_real)) ) gradient_real = jnp.concatenate( (jnp.real(gradient_real), jnp.imag(gradient_real)) ) return jnp.sum(descent_dir_real * gradient_real) @jit def _line_search_new_tensors(peps_tensors, descent_dir, alpha): return [peps_tensors[i] + alpha * descent_dir[i] for i in range(len(peps_tensors))] def _get_new_unitcell( new_tensors, unitcell, spiral_indices, convert_to_unitcell_func, generate_unitcell, reinitialize_env_as_identities, ): if spiral_indices is not None: for i in spiral_indices: if ( varipeps_config.spiral_wavevector_type is Wavevector_Type.TWO_PI_POSITIVE_ONLY ): new_tensors[i] = new_tensors[i] % 2 elif ( varipeps_config.spiral_wavevector_type is Wavevector_Type.TWO_PI_SYMMETRIC ): new_tensors[i] = new_tensors[i] % 4 - 2 else: raise ValueError("Unknown wavevector type!") if convert_to_unitcell_func is None or generate_unitcell: unitcell_tensors = unitcell.get_unique_tensors() new_unitcell = unitcell.replace_unique_tensors( [ unitcell_tensors[i].replace_tensor( new_tensors[i], reinitialize_env_as_identities=reinitialize_env_as_identities, ) for i in range(unitcell.get_len_unique_tensors()) ] ) else: new_unitcell = None return new_tensors, new_unitcell @jit def _armijo_value(current_val, descent_dir, gradient, alpha, const_factor): descent_dir_real, _ = ravel_pytree(descent_dir) gradient_real, _ = ravel_pytree(gradient) if jnp.iscomplexobj(descent_dir_real): descent_dir_real = jnp.concatenate( (jnp.real(descent_dir_real), jnp.imag(descent_dir_real)) ) gradient_real = jnp.concatenate( (jnp.real(gradient_real), jnp.imag(gradient_real)) ) return jnp.fmin( current_val, current_val + const_factor * alpha * jnp.sum(descent_dir_real * gradient_real), ) @jit def _wolfe_value( current_val, descent_dir, gradient, new_gradient, alpha, armijo_const_factor, wolfe_const_factor, ): descent_dir_real, _ = ravel_pytree(descent_dir) gradient_real, _ = ravel_pytree(gradient) new_gradient_real, _ = ravel_pytree(new_gradient) if jnp.iscomplexobj(descent_dir_real): descent_dir_real = jnp.concatenate( (jnp.real(descent_dir_real), jnp.imag(descent_dir_real)) ) gradient_real = jnp.concatenate( (jnp.real(gradient_real), jnp.imag(gradient_real)) ) new_gradient_real = jnp.concatenate( (jnp.real(new_gradient_real), jnp.imag(new_gradient_real)) ) scalar_descent_grad = jnp.sum(descent_dir_real * gradient_real) cmp_value = current_val + armijo_const_factor * alpha * scalar_descent_grad scalar_descent_new_grad = jnp.sum(descent_dir_real * new_gradient_real) strong_wolfe_left_side = -scalar_descent_new_grad strong_wolfe_right_side = -wolfe_const_factor * scalar_descent_grad return ( cmp_value, strong_wolfe_left_side, strong_wolfe_right_side, scalar_descent_new_grad, ) @jit def _wolfe_new_alpha( alpha, last_alpha, value, last_value, descent_grad, descent_last_grad, lower_bound, upper_bound, ): d1 = ( descent_last_grad + descent_grad - 3 * (last_value - value) / (last_alpha - alpha) ) d2 = jnp.sign(alpha - last_alpha) * jnp.sqrt( d1**2 - descent_last_grad * descent_grad ) new_alpha = alpha - (alpha - last_alpha) * (descent_grad + d2 - d1) / ( descent_grad - descent_last_grad + 2 * d2 ) return jnp.where( jnp.isinf(value) | jnp.isinf(last_value) | (new_alpha <= lower_bound) | (new_alpha >= upper_bound) | jnp.isnan(new_alpha), lower_bound + (upper_bound - lower_bound) / 2, new_alpha, ) @jit def _hager_zhang_initial_zero(input_tensors, gradient, config): input_tensors_real, _ = ravel_pytree(input_tensors) gradient_real, _ = ravel_pytree(gradient) if jnp.iscomplexobj(input_tensors_real): input_tensors_real = jnp.concatenate( (jnp.real(input_tensors_real), jnp.imag(input_tensors_real)) ) gradient_real = jnp.concatenate( (jnp.real(gradient_real), jnp.imag(gradient_real)) ) result = config.line_search_hager_zhang_psi_0 result *= jnp.linalg.norm(input_tensors_real, ord=jnp.inf) result /= jnp.linalg.norm(gradient_real, ord=jnp.inf) result = jnp.where(result == 0, config.line_search_initial_step_size, result) return result class _Hager_Zhang_Initial_State(enum.Enum): NOT_FOUND = enum.auto() FOUND = enum.auto() SCALAR_LOWER_VALUE_GREATER = enum.auto() class _Hager_Zhang_State(enum.Enum): NONE = enum.auto() UPDATE = enum.auto() UPDATE_INNER = enum.auto() @jit def _hager_zhang_initial_quad_step_inner( old_value, new_value, gradient, descent_direction, alpha, fallback_alpha ): g_d_term = _scalar_descent_grad(descent_direction, gradient) sum_term = old_value + alpha * g_d_term sum_term -= new_value alpha = jnp.where( sum_term < 0, alpha**2 * g_d_term / (2 * sum_term), fallback_alpha ) alpha = jnp.where(alpha > 0, alpha, fallback_alpha) return alpha def _hager_zhang_initial_quad_step( input_tensors, unitcell, gradient, descent_direction, old_alpha, old_value, spiral_indices, convert_to_unitcell_func, generate_unitcell, expectation_func, additional_input, reinitialize_env_as_identities, enforce_elementwise_convergence, ): alpha = varipeps_config.line_search_hager_zhang_psi_1 * old_alpha new_tensors = _line_search_new_tensors(input_tensors, descent_direction, alpha) new_tensors, new_unitcell = _get_new_unitcell( new_tensors, unitcell, spiral_indices, convert_to_unitcell_func, generate_unitcell, reinitialize_env_as_identities, ) new_value, (new_unitcell, _) = calc_ctmrg_expectation( new_tensors, new_unitcell, expectation_func, convert_to_unitcell_func, additional_input, enforce_elementwise_convergence=enforce_elementwise_convergence, ) fallback_alpha = varipeps_config.line_search_hager_zhang_psi_2 * old_alpha return jnp.where( new_value <= old_value, _hager_zhang_initial_quad_step_inner( old_value, new_value, gradient, descent_direction, alpha, fallback_alpha ), fallback_alpha, ) class NoSuitableStepSizeError(Exception): pass def line_search( input_tensors: Sequence[jnp.ndarray], unitcell: PEPS_Unit_Cell, expectation_func: Expectation_Model, gradient: jnp.ndarray, descent_direction: jnp.ndarray, current_value: Union[float, jnp.ndarray], last_step_size: Optional[Union[float, jnp.ndarray]] = None, convert_to_unitcell_func: Optional[Map_To_PEPS_Model] = None, generate_unitcell: bool = False, spiral_indices: Optional[Sequence[int]] = None, additional_input: Dict[str, jnp.ndarray] = {}, reinitialize_env_as_identities: bool = True, ) -> Tuple[ List[jnp.ndarray], PEPS_Unit_Cell, Union[float, jnp.ndarray], Union[float, jnp.ndarray], ]: """ Run two-way backtracing line search method for the CTMRG routine. Args: input_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`): Sequence of the current tensors which should be optimized. unitcell (:obj:`~varipeps.peps.PEPS_Unit_Cell`): The PEPS unitcell to work on. expectation_func (:obj:`~varipeps.expectation.Expectation_Model`): Callable to calculate one expectation value which is used as loss loss function of the model. Likely the function to calculate the energy. gradient (:obj:`jax.numpy.ndarray`): The gradient of the CTMRG method and expectation function for the current step. descent_direction (:obj:`jax.numpy.ndarray`): The descent direction which should be used for the line search. current_value (:obj:`float` or :obj:`jax.numpy.ndarray`): The current value of the evaluation of the expectation function. last_step_size (:obj:`float` or :obj:`jax.numpy.ndarray`): The step size found in the last line search. convert_to_unitcell_func (:obj:`~varipeps.mapping.Map_To_PEPS_Model`): Function to convert the `input_tensors` to a PEPS unitcell. If ommited, it is assumed that a PEPS unitcell is the input. generate_unitcell (:obj:`bool`): Force generation of unitcell from new tensors spiral_indices (:term:`sequence` of :obj:`int`): If spiral iPEPS ansatz is used, this argument contains the indices of the wave vectors in the input tensor list. additional_input (:obj:`dict` of :obj:`str` to :obj:`jax.numpy.ndarray` mapping): Dict with additional inputs which should be considered in the calculation of the expectation value. reinitialize_env_as_identities (:obj:`bool`): Flag if the env tensors should be reinitialized with identities. Returns: :obj:`tuple`\ (:obj:`list`\ (:obj:`jax.numpy.ndarray`), :obj:`~varipeps.peps.PEPS_Unit_Cell`, :obj:`float`, :obj:`float`): Tuple with the optimized tensors, the new unitcell, the reduced expectation value and the step size found in the line search. Raises: :obj:`ValueError`: The parameters mismatch the expected inputs. :obj:`RuntimeError`: The line search does not converge. """ has_been_increased = False incrementation_not_helped = False enforce_elementwise_convergence = ( varipeps_config.ctmrg_enforce_elementwise_convergence or varipeps_config.ad_use_custom_vjp ) if varipeps_config.line_search_method is Line_Search_Methods.HAGERZHANG: if last_step_size is None or last_step_size <= 0: alpha = _hager_zhang_initial_zero(input_tensors, gradient, varipeps_config) elif varipeps_config.line_search_hager_zhang_quad_step: try: alpha = _hager_zhang_initial_quad_step( input_tensors, unitcell, gradient, descent_direction, last_step_size, current_value, spiral_indices, convert_to_unitcell_func, generate_unitcell, expectation_func, additional_input, reinitialize_env_as_identities, enforce_elementwise_convergence, ) except CTMRGNotConvergedError: alpha = varipeps_config.line_search_hager_zhang_psi_2 * last_step_size else: alpha = varipeps_config.line_search_hager_zhang_psi_2 * last_step_size else: alpha = ( last_step_size if last_step_size is not None and varipeps_config.line_search_use_last_step_size and last_step_size > 0 else varipeps_config.line_search_initial_step_size ) wolfe_upper_bound = None wolfe_lower_bound = None wolfe_alpha_last_step = 0 wolfe_descent_new_grad = _scalar_descent_grad(descent_direction, gradient) hager_zhang_lower_bound = 0 hager_zhang_lower_bound_value = current_value hager_zhang_lower_bound_grad = gradient hager_zhang_lower_bound_des_grad = wolfe_descent_new_grad hager_zhang_upper_bound = alpha hager_zhang_upper_bound_value = None hager_zhang_upper_bound_grad = None hager_zhang_upper_bound_des_grad = None hager_zhang_alpha_last_step = 0 hager_zhang_initial_found = _Hager_Zhang_Initial_State.NOT_FOUND hager_zhang_descent_grad = wolfe_descent_new_grad hager_zhang_state = _Hager_Zhang_State.NONE hager_zhang_eps = ( jnp.linalg.norm(ravel_pytree(gradient)[0]) * varipeps_config.line_search_hager_zhang_eps_grad_norm_factor if varipeps_config.line_search_hager_zhang_eps_use_grad_norm else varipeps_config.line_search_hager_zhang_eps ) new_value = current_value tmp_value = None tmp_unitcell = None tmp_gradient = None tmp_descent_direction = None signal_reset_descent_dir = False cache_original_unitcell = { unitcell[0, 0][0][0].chi: (unitcell, gradient, descent_direction, current_value) } max_trunc_error = jnp.nan count = 0 while count < varipeps_config.line_search_max_steps: new_tensors = _line_search_new_tensors(input_tensors, descent_direction, alpha) new_tensors, new_unitcell = _get_new_unitcell( new_tensors, unitcell, spiral_indices, convert_to_unitcell_func, generate_unitcell, reinitialize_env_as_identities, ) if ( varipeps_config.line_search_method is Line_Search_Methods.SIMPLE or varipeps_config.line_search_method is Line_Search_Methods.ARMIJO ): try: new_value, (new_unitcell, max_trunc_error) = calc_ctmrg_expectation( new_tensors, new_unitcell, expectation_func, convert_to_unitcell_func, additional_input, enforce_elementwise_convergence=enforce_elementwise_convergence, ) if new_unitcell[0, 0][0][0].chi > unitcell[0, 0][0][0].chi: tmp_value = current_value tmp_unitcell = unitcell tmp_gradient = gradient tmp_descent_direction = descent_direction if ( cache_original_unitcell.get(new_unitcell[0, 0][0][0].chi) is not None ): ( unitcell, gradient, descent_direction, current_value, ) = cache_original_unitcell[new_unitcell[0, 0][0][0].chi] else: unitcell = unitcell.change_chi(new_unitcell[0, 0][0][0].chi) debug_print( "Line search: Recalculate original unitcell with higher chi {}.", new_unitcell[0, 0][0][0].chi, ) if varipeps_config.ad_use_custom_vjp: ( current_value, (unitcell, max_trunc_error), ), tmp_gradient_seq = calc_ctmrg_expectation_custom_value_and_grad( input_tensors, unitcell, expectation_func, convert_to_unitcell_func, additional_input, ) else: ( current_value, (unitcell, max_trunc_error), ), tmp_gradient_seq = calc_preconverged_ctmrg_value_and_grad( input_tensors, unitcell, expectation_func, convert_to_unitcell_func, additional_input, calc_preconverged=True, ) gradient = [elem.conj() for elem in tmp_gradient_seq] descent_direction = [-elem for elem in tmp_gradient] cache_original_unitcell[new_unitcell[0, 0][0][0].chi] = ( unitcell, gradient, descent_direction, current_value, ) signal_reset_descent_dir = True except CTMRGNotConvergedError: new_value = jnp.inf elif ( varipeps_config.line_search_method is Line_Search_Methods.WOLFE or varipeps_config.line_search_method is Line_Search_Methods.HAGERZHANG ): wolfe_value_last_step = new_value try: if varipeps_config.ad_use_custom_vjp: ( new_value, (new_unitcell, max_trunc_error), ), new_gradient_seq = calc_ctmrg_expectation_custom_value_and_grad( new_tensors, new_unitcell, expectation_func, convert_to_unitcell_func, additional_input, ) else: ( new_value, (new_unitcell, max_trunc_error), ), new_gradient_seq = calc_preconverged_ctmrg_value_and_grad( new_tensors, new_unitcell, expectation_func, convert_to_unitcell_func, additional_input, calc_preconverged=True, ) new_gradient = [elem.conj() for elem in new_gradient_seq] if new_unitcell[0, 0][0][0].chi > unitcell[0, 0][0][0].chi: tmp_value = current_value tmp_unitcell = unitcell tmp_gradient = gradient tmp_descent_direction = descent_direction if ( cache_original_unitcell.get(new_unitcell[0, 0][0][0].chi) is not None ): ( unitcell, gradient, descent_direction, current_value, ) = cache_original_unitcell[new_unitcell[0, 0][0][0].chi] else: unitcell = unitcell.change_chi(new_unitcell[0, 0][0][0].chi) debug_print( "Line search: Recalculate original unitcell with higher chi {}.", new_unitcell[0, 0][0][0].chi, ) if varipeps_config.ad_use_custom_vjp: ( current_value, (unitcell, max_trunc_error), ), tmp_gradient_seq = calc_ctmrg_expectation_custom_value_and_grad( input_tensors, unitcell, expectation_func, convert_to_unitcell_func, additional_input, ) else: ( current_value, (unitcell, max_trunc_error), ), tmp_gradient_seq = calc_preconverged_ctmrg_value_and_grad( input_tensors, unitcell, expectation_func, convert_to_unitcell_func, additional_input, calc_preconverged=True, ) gradient = [elem.conj() for elem in tmp_gradient_seq] descent_direction = [-elem for elem in tmp_gradient] cache_original_unitcell[new_unitcell[0, 0][0][0].chi] = ( unitcell, gradient, descent_direction, current_value, ) signal_reset_descent_dir = True except (CTMRGNotConvergedError, CTMRGGradientNotConvergedError): new_value = jnp.inf new_gradient = gradient else: raise ValueError("Unknown line search method.") if varipeps_config.line_search_method is Line_Search_Methods.HAGERZHANG: descent_new_grad = _scalar_descent_grad(descent_direction, new_gradient) hz_wolfe_1_left = ( varipeps_config.line_search_hager_zhang_delta * hager_zhang_descent_grad ) hz_wolfe_1_right = (new_value - current_value) / alpha hz_wolfe_2_right = ( varipeps_config.line_search_hager_zhang_sigma * hager_zhang_descent_grad ) if descent_new_grad >= hz_wolfe_2_right: if hz_wolfe_1_left >= hz_wolfe_1_right and new_value <= ( current_value + hager_zhang_eps ): break hz_approx_wolfe_left = ( 2 * varipeps_config.line_search_hager_zhang_delta - 1 ) * hager_zhang_descent_grad if hz_approx_wolfe_left >= hager_zhang_descent_grad and new_value <= ( current_value + hager_zhang_eps ): break if ( varipeps_config.line_search_method is Line_Search_Methods.HAGERZHANG and hager_zhang_initial_found is not _Hager_Zhang_Initial_State.FOUND ): if ( hager_zhang_initial_found is _Hager_Zhang_Initial_State.SCALAR_LOWER_VALUE_GREATER ): if descent_new_grad >= 0: hager_zhang_upper_bound = alpha hager_zhang_upper_bound_value = new_value hager_zhang_upper_bound_grad = new_gradient hager_zhang_upper_bound_des_grad = descent_new_grad hager_zhang_initial_found = _Hager_Zhang_Initial_State.FOUND elif new_value <= (current_value + hager_zhang_eps): hager_zhang_lower_bound = alpha hager_zhang_lower_bound_value = new_value hager_zhang_lower_bound_grad = new_gradient hager_zhang_lower_bound_des_grad = descent_new_grad alpha = ( (1 - varipeps_config.line_search_hager_zhang_theta) * hager_zhang_lower_bound + varipeps_config.line_search_hager_zhang_theta * hager_zhang_upper_bound ) if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 continue else: hager_zhang_upper_bound = alpha hager_zhang_upper_bound_value = new_value hager_zhang_upper_bound_grad = new_gradient hager_zhang_upper_bound_des_grad = descent_new_grad alpha = ( (1 - varipeps_config.line_search_hager_zhang_theta) * hager_zhang_lower_bound + varipeps_config.line_search_hager_zhang_theta * hager_zhang_upper_bound ) if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 continue elif descent_new_grad >= 0: hager_zhang_upper_bound = alpha hager_zhang_upper_bound_value = new_value hager_zhang_upper_bound_grad = new_gradient hager_zhang_upper_bound_des_grad = descent_new_grad hager_zhang_initial_found = _Hager_Zhang_Initial_State.FOUND elif descent_new_grad < 0 and new_value > (current_value + hager_zhang_eps): alpha = varipeps_config.line_search_hager_zhang_theta * alpha hager_zhang_initial_found = ( _Hager_Zhang_Initial_State.SCALAR_LOWER_VALUE_GREATER ) if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 continue else: if new_value <= (current_value + hager_zhang_eps): hager_zhang_lower_bound = alpha hager_zhang_lower_bound_value = new_value hager_zhang_lower_bound_grad = new_gradient hager_zhang_lower_bound_des_grad = descent_new_grad alpha *= varipeps_config.line_search_hager_zhang_rho if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 continue if varipeps_config.line_search_method is Line_Search_Methods.SIMPLE: smaller_value_found = ( new_value <= current_value or (new_value - current_value) <= 1e-13 ) elif varipeps_config.line_search_method is Line_Search_Methods.ARMIJO: cmp_value = _armijo_value( current_value, descent_direction, gradient, alpha, varipeps_config.line_search_armijo_const, ) smaller_value_found = ( new_value <= cmp_value or (new_value - cmp_value) <= 1e-13 ) elif varipeps_config.line_search_method is Line_Search_Methods.WOLFE: wolfe_descent_last_grad = wolfe_descent_new_grad ( cmp_value, wolfe_left_side, wolfe_right_side, wolfe_descent_new_grad, ) = _wolfe_value( current_value, descent_direction, gradient, new_gradient, alpha, varipeps_config.line_search_armijo_const, varipeps_config.line_search_wolfe_const, ) wolfe_cond_1 = new_value <= cmp_value or (new_value - cmp_value) <= 1e-13 wolfe_cond_2 = ( wolfe_left_side <= wolfe_right_side or (wolfe_left_side - wolfe_right_side) <= 1e-13 ) if ( varipeps_config.line_search_method is Line_Search_Methods.SIMPLE or varipeps_config.line_search_method is Line_Search_Methods.ARMIJO ): if smaller_value_found: if ( alpha >= varipeps_config.line_search_initial_step_size or incrementation_not_helped ): break has_been_increased = True alpha /= varipeps_config.line_search_reduction_factor else: if has_been_increased: incrementation_not_helped = True alpha = varipeps_config.line_search_reduction_factor * alpha elif varipeps_config.line_search_method is Line_Search_Methods.WOLFE: if wolfe_upper_bound is None and wolfe_lower_bound is None: if jnp.isinf(new_value): alpha /= varipeps_config.line_search_reduction_factor elif not wolfe_cond_1 or ( count > 0 and new_value >= wolfe_value_last_step ): wolfe_lower_bound = wolfe_alpha_last_step wolfe_lower_bound_value = wolfe_value_last_step wolfe_upper_bound = alpha wolfe_upper_bound_value = new_value tmp_alpha = alpha alpha = _wolfe_new_alpha( alpha, wolfe_alpha_last_step, new_value, wolfe_value_last_step, wolfe_descent_new_grad, wolfe_descent_last_grad, jnp.fmin(wolfe_lower_bound, wolfe_upper_bound), jnp.fmax(wolfe_lower_bound, wolfe_upper_bound), ) wolfe_alpha_last_step = tmp_alpha elif wolfe_cond_2: break elif wolfe_descent_new_grad >= 0: wolfe_lower_bound = alpha wolfe_lower_bound_value = new_value wolfe_upper_bound = wolfe_alpha_last_step wolfe_upper_bound_value = wolfe_value_last_step tmp_alpha = alpha alpha = _wolfe_new_alpha( alpha, wolfe_alpha_last_step, new_value, wolfe_value_last_step, wolfe_descent_new_grad, wolfe_descent_last_grad, jnp.fmin(wolfe_lower_bound, wolfe_upper_bound), jnp.fmax(wolfe_lower_bound, wolfe_upper_bound), ) wolfe_alpha_last_step = tmp_alpha else: wolfe_alpha_last_step = alpha alpha /= varipeps_config.line_search_reduction_factor elif jnp.isinf(new_value): alpha = alpha + (wolfe_upper_bound - alpha) / 2 else: if new_value > cmp_value or new_value >= wolfe_lower_bound_value: wolfe_upper_bound = alpha wolfe_upper_bound_value = new_value else: if wolfe_cond_2: break if ( wolfe_descent_new_grad * (wolfe_upper_bound - wolfe_lower_bound) >= 0 ): wolfe_upper_bound = wolfe_lower_bound wolfe_upper_bound_value = wolfe_lower_bound_value wolfe_lower_bound = alpha wolfe_lower_bound_value = new_value tmp_alpha = alpha alpha = _wolfe_new_alpha( alpha, wolfe_alpha_last_step, new_value, wolfe_value_last_step, wolfe_descent_new_grad, wolfe_descent_last_grad, jnp.fmin(wolfe_lower_bound, wolfe_upper_bound), jnp.fmax(wolfe_lower_bound, wolfe_upper_bound), ) wolfe_alpha_last_step = tmp_alpha elif varipeps_config.line_search_method is Line_Search_Methods.HAGERZHANG: if hager_zhang_state is _Hager_Zhang_State.UPDATE: if descent_new_grad >= 0: hager_zhang_upper_bound = alpha hager_zhang_upper_bound_value = new_value hager_zhang_upper_bound_grad = new_gradient hager_zhang_upper_bound_des_grad = descent_new_grad hager_zhang_state = _Hager_Zhang_State.NONE elif new_value <= (current_value + hager_zhang_eps): hager_zhang_lower_bound = alpha hager_zhang_lower_bound_value = new_value hager_zhang_lower_bound_grad = new_gradient hager_zhang_lower_bound_des_grad = descent_new_grad hager_zhang_state = _Hager_Zhang_State.NONE else: hager_zhang_upper_bound = alpha hager_zhang_upper_bound_value = new_value hager_zhang_upper_bound_grad = new_gradient hager_zhang_upper_bound_des_grad = _scalar_descent_grad( descent_direction, new_gradient ) alpha = ( (1 - varipeps_config.line_search_hager_zhang_theta) * hager_zhang_lower_bound + varipeps_config.line_search_hager_zhang_theta * hager_zhang_upper_bound ) hager_zhang_state = _Hager_Zhang_State.UPDATE_INNER if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 continue elif hager_zhang_state is _Hager_Zhang_State.UPDATE_INNER: if descent_new_grad >= 0: hager_zhang_upper_bound = alpha hager_zhang_upper_bound_value = new_value hager_zhang_upper_bound_grad = new_gradient hager_zhang_upper_bound_des_grad = descent_new_grad hager_zhang_state = _Hager_Zhang_State.NONE elif new_value <= (current_value + hager_zhang_eps): hager_zhang_lower_bound = alpha hager_zhang_lower_bound_value = new_value hager_zhang_lower_bound_grad = new_gradient hager_zhang_lower_bound_des_grad = descent_new_grad alpha = ( (1 - varipeps_config.line_search_hager_zhang_theta) * hager_zhang_lower_bound + varipeps_config.line_search_hager_zhang_theta * hager_zhang_upper_bound ) if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 continue else: hager_zhang_upper_bound = alpha hager_zhang_upper_bound_value = new_value hager_zhang_upper_bound_grad = new_gradient hager_zhang_upper_bound_des_grad = _scalar_descent_grad( descent_direction, new_gradient ) alpha = ( (1 - varipeps_config.line_search_hager_zhang_theta) * hager_zhang_lower_bound + varipeps_config.line_search_hager_zhang_theta * hager_zhang_upper_bound ) if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 continue else: alpha = hager_zhang_lower_bound * hager_zhang_upper_bound_des_grad alpha -= hager_zhang_upper_bound * hager_zhang_lower_bound_des_grad alpha /= ( hager_zhang_upper_bound_des_grad - hager_zhang_lower_bound_des_grad ) if alpha <= 0: tqdm.write("Found negative alpha in secant operation!") hz_secant_alpha = alpha hz_secant_lower = hager_zhang_lower_bound hz_secant_lower_value = hager_zhang_lower_bound_value hz_secant_lower_grad = hager_zhang_lower_bound_grad hz_secant_lower_des_grad = hager_zhang_lower_bound_des_grad hz_secant_upper = hager_zhang_upper_bound hz_secant_upper_value = hager_zhang_upper_bound_value hz_secant_upper_grad = hager_zhang_upper_bound_grad hz_secant_upper_des_grad = hager_zhang_upper_bound_des_grad if hager_zhang_lower_bound < alpha < hager_zhang_upper_bound: hager_zhang_state = _Hager_Zhang_State.UPDATE if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 continue if hz_secant_alpha is not None and ( hz_secant_alpha == hager_zhang_lower_bound or hz_secant_alpha == hager_zhang_upper_bound ): if hz_secant_alpha == hager_zhang_lower_bound: alpha = hz_secant_lower * hager_zhang_lower_bound_des_grad alpha -= hager_zhang_lower_bound * hz_secant_lower_des_grad alpha /= hager_zhang_lower_bound_des_grad - hz_secant_lower_des_grad else: alpha = hz_secant_upper * hager_zhang_upper_bound_des_grad alpha -= hager_zhang_upper_bound * hz_secant_upper_des_grad alpha /= hager_zhang_upper_bound_des_grad - hz_secant_upper_des_grad hz_secant_alpha = None if hager_zhang_lower_bound < alpha < hager_zhang_upper_bound: hager_zhang_state = _Hager_Zhang_State.UPDATE if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 continue hz_secant_alpha = None if hz_secant_lower is not None and ( (hager_zhang_upper_bound - hager_zhang_lower_bound) > varipeps_config.line_search_hager_zhang_gamma * (hz_secant_upper - hz_secant_lower) ): alpha = (hager_zhang_lower_bound + hager_zhang_upper_bound) / 2 hz_secant_lower = None hager_zhang_state = _Hager_Zhang_State.UPDATE if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 continue hz_secant_lower = None if tmp_value is not None: current_value, unitcell, gradient, descent_direction = ( tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction, ) tmp_value, tmp_unitcell, tmp_gradient, tmp_descent_direction = ( None, None, None, None, ) signal_reset_descent_dir = False count += 1 if ( new_unitcell is not None and new_unitcell[0, 0][0][0].chi != unitcell[0, 0][0][0].chi ): jax.clear_caches() if count == varipeps_config.line_search_max_steps: raise NoSuitableStepSizeError(f"Count {count}, Last alpha {alpha}") return ( new_tensors, new_unitcell, new_value, alpha, signal_reset_descent_dir, max_trunc_error, )